Konna Mayor Sory Diakite told The Associated Press that 20 bodies had been recovered by midday.
At least 400 passengers were believed to have been onboard the vessel, though only 210 survivors had been counted, he said.
Family members in the capital of Bamako said they had received confirmation of the accident as well.
"The boat sank around 8 pm between Mopti and Konna," said Abouri Djittey, a resident of Bamako. "It was a survivor who called me around 9 pm to tell me that my pregnant daughter and her friend had both drowned."
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"For the moment, the conditions of what exactly happened are not known," he said.
Large boats carry hundreds of passengers on the Niger River at this time of year.
While most Malians cannot swim, travel by water is preferable to journeying on the poor roads across Mali's desert north.